"Kubla Khan" is a fragment because the author plainly stated to friends that there was more, but it could not be written down because it was lost to a business sales call.
Coleridge had taken a tonic which probably contained some form of opium. He was reading some poetry when he dozed off. Opium tonics are noted for producing vivid dreams. Upon awakening, Coleridge began to write down what he had dreamed.
Someone knocked at his door. Colderdge answered it and was detained for over an hour. When Coleridge went back to his desk to finish the poem, it was gone.
Coleridge's poem Kubla Khan is called a 'fragment' primarily bacause the poet himself chose to call it a fragment of a fuller composition in a state of dream, an account of which was supplied in a prefatory note to the piece on its publication in 1816, some nineteen years after its so-called mysterious genesis. The issue has been strongly debated ever since, and though the poem shows some elements of dream and a somewhat abrupt end, it is still simplistic to call it a fragment for it does not show any incoherence of construction or illogicality of thought. The centrality of the image of Kubla's 'pleasure-dome' through all the three stanzas of the poem holding the thought-process metaphorically together, Coleridge's natural-supernatural imagery, the thematic link between the two sections inspite of the geographical switch from Kubla's earthly paradise in section 1 to the song of the Abyssinian maid, & the poem culminating into a dicourse on the ontology of poetry rather suggest that by calling Kubla Khan a 'vision in a dream, a fragment', Coleridge palyed into the hands of critics.